i2n-3+i2n-1+i2n+1+i2n+3的值为()A.-2B.0C.2D.4-数学

题目简介

i2n-3+i2n-1+i2n+1+i2n+3的值为()A.-2B.0C.2D.4-数学

题目详情

i2n-3+i2n-1+i2n+1+i2n+3的值为(  )
A.-2B.0C.2D.4
题型:单选题难度:中档来源:不详

答案

因为i4n=1,i4n+1=i,i4n+2=-1,i4n+3=-i;由复数i2n-3+i2n-1+i2n+1+i2n+3=2(i2n+1+i2n+3),
当n是偶数时2(i2n+1+i2n+3)=2(i+i3)=0;当n是奇数时2(i2n+1+i2n+3)=2(i3+i)=0.
故选B.

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